Finite Group Databasebeta

← #10845977

Subgroups — #10845977

Order 768.

1084 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#82779C211yesmaximal, characteristic, complemented
2C2×#5049C211yesmaximal, characteristic, complemented
3C2×#4865C211yesmaximal, characteristic, complemented
4C2×#4819C211yesmaximal, characteristic, complemented
5C2×#4729C211yesmaximal, characteristic, complemented
6#73933C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8#70564C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70271C211yesmaximal, characteristic, complemented
11#70226C211yesmaximal, characteristic, complemented
12#69961C211yesmaximal, characteristic, complemented
13#69517C211yesmaximal, characteristic, complemented
14#68822C211yesmaximal, characteristic, complemented
15#68780C211yesmaximal, characteristic, complemented
16#25390—31nomaximal, Sylow
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×#947C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C2×#930C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C22×D24C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C3×#380C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#821C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×Dic3⋊C8C2211yescharacteristic
40C2×C8×Dic3C2211yescharacteristic
41#5049—24no—
42#4993—21no—
43#4988—21no—
44#4987C2211yescharacteristic
45#4977C2211yescharacteristic
46Dic3×C4⋊C4C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4960—21no—
52#4960—21no—
53#4957—21no—
54#4956—21no—
55#4865—24no—
56#4819—24no—
57#4729—24no—
58#4675—21no—
59#4665—21no—
60C3×#340C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#469—31no—
65C2×#468—31no—
66C2×#463—31no—
67C2×#436—31no—
68#2540—31no—
69#2535—31no—
70#2035D311yescharacteristic, complemented
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1958—31no—
75#1949—31no—
76#1895—31no—
77#1894—31no—
78C4×#102—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C22×#67D411yescharacteristic
84C22×D12—21no—
85C22×D12—21no—
86C22×D12C2311yescharacteristic
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—41no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×#217D411yescharacteristic
101#947—22no—
102#947—22no—
103#946—22no—
104#946—41no—
105C2×#215—22no—
106C2×#215—22no—
107C2×#215—41no—
108#930—22no—
109#930—22no—
110#930—41no—
111#930—41no—
112C4×#67—22no—
113C4×#67—22no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4D411yescharacteristic
128C2×C4×Dic3—21no—
129C2×C4×Dic3C2311yescharacteristic
130C2×#208—22no—
131C2×#208—22no—
132C2×#208—41no—
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C2×D24—22no—
136C2×D24—22no—
137C2×D24—41no—
138C2×ΓL(1,𝔽25)—22no—
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)—41no—
141#895—22no—
142#895—22no—
143#895—41no—
144#895—41no—
145#893—22no—
146#893—22no—
147C3×#106—22no—
148C3×#103—22no—
149C3×#103—41no—
150C3×C22⋊C8—22no—
151C3×#95—21no—
152#835—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#821—22no—
158#821—41no—
159(C2×D3)⋊C8—22no—
160Dic3⋊C8D414yescomplemented
161C8×Dic3—22no—
162#809—22no—
163#809—22no—
164#809D414yescomplemented
165#807—22no—
166C22×SD16—31no—
167C22×D8—31no—
168C22×M16—31no—
169C22×M16—31no—
170C2×#124—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8C2×D311yescharacteristic
173C2×#121—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179#469—64no—
180#468—64no—
181#463—64no—
182#436—64no—
183C2×#107—31no—
184C2×#106C2×D311yescharacteristic
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103C2×D311yescharacteristic
188C2×#103C2×D311yescharacteristic
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8C2×D311yescharacteristic
196C2×C4×C8—31no—
197#399—61no—
198#397—61no—
199#392—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#386—61no—
204#386—61no—
205#382—31no—
206#380—31no—
207#380C2×D311yescharacteristic
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340C2×D311yescharacteristic
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C23×D3—21no—
216C23×D3C2×D411yescharacteristic
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2411yescharacteristic
235C2×#67—22no—
236C2×#67—41no—
237C2×#67—41no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—81no—
243C2×#67—81no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3C2×D411yescharacteristic
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—42no—
261C2×D12—42no—
262C2×D12—42no—
263C2×D12—42no—
264C2×D12—81no—
265C2×D12—81no—
266C2×D12C2×D412yes—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—42no—
274C2×C4×D3—81no—
275C2×C4×D3—81no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8C2×D412yes—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—42no—
288C3×C4⋊C4C2×D412yes—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—81no—
291#217—22no—
292#215—44no—
293(C2×D3)⋊C4—22no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—81no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3#4112yes—
307Dic3⋊C4—22no—
308Dic3⋊C4—42no—
309C4×Dic3—81no—
310C4×Dic3C2×D412yes—
311C4×Dic3#4112yes—
312#208—44no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8C2×D412yes—
318C2×C3⋊C8C2×D412yes—
319D24—44no—
320ΓL(1,𝔽25)—44no—
321C22×Q8C22×D311yescharacteristic
322C22×D4—31no—
323C22×D4—31no—
324C22×D4—31no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4—61no—
328C22×D4—61no—
329C23×C4—31no—
330C23×C4—61no—
331C23×C4C22×D311yescharacteristic
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—121no—
335C2×D8—62no—
336C2×D8—62no—
337C2×D8—121no—
338C2×M16—62no—
339C2×M16—62no—
340C2×M16—62no—
341C2×M16—62no—
342C2×M16—121no—
343C2×M16—121no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8C22×D311yescharacteristic
347C22×C8C22×D311yescharacteristic
348#124—62no—
349#124—62no—
350C22⋊Q8—22no—
351C22⋊Q8—41no—
352C22⋊Q8—62no—
353C22⋊Q8—121no—
354#121—62no—
355#121—62no—
356#121—62no—
357#121—62no—
358#121—121no—
359#121—121no—
360#121—121no—
361#121—121no—
362C4×D4—62no—
363C4×D4—62no—
364C4×D4—62no—
365C4×D4—62no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C42—31no—
388C2×C42—61no—
389#107—62no—
390#106—22no—
391C4⋊C8—34no—
392#103—22no—
393#103—41no—
394#103—62no—
395#102—34no—
396#102—62no—
397#102—62no—
398#102—62no—
399#102—121no—
400C22⋊C8—22no—
401C22⋊C8—62no—
402C4×C8—62no—
403#95—21no—
404#95—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3C22×D411yescharacteristic
416C22×D3—21no—
417C22×D3—22no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×Q8—41no—
438C3×Q8—41no—
439C3×Q8—41no—
440C3×Q8—41no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465C2×C3×C4H(5,𝔽2)11yescharacteristic
466#67—44no—
467#67—84no—
468#67—84no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3#12112yes—
483C2×Dic3#12112yes—
484D12—22no—
485D12—22no—
486D12—41no—
487D12—41no—
488D12—41no—
489D12—41no—
490D12—41no—
491D12—41no—
492D12—84no—
493D12—84no—
494C4×D3—41no—
495C4×D3—41no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—84no—
499C3×C8—22no—
500C3×C8—41no—
501C3⋊C8—22no—
502C3⋊C8—22no—
503C24—31no—
504C24—61no—
505C24—61no—
506C24D3×D411yescharacteristic
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×D4—32no—
514C2×D4—62no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—122no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—121no—
531C2×D4—121no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—241no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4—241no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—122no—
562C22×C4—241no—
563C22×C4—241no—
564C22×C4D3×D411yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—124no—
567D8—124no—
568M16—124no—
569M16—124no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—32no—
576C2×C8—32no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8D3×D412yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—32no—
588C4⋊C4—42no—
589C4⋊C4—62no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—122no—
594C4⋊C4D3×D412yes—
595C22⋊C4—42no—
596C22⋊C4—62no—
597C22⋊C4—62no—
598C22⋊C4—81no—
599C22⋊C4—122no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—122no—
607C22⋊C4—241no—
608C42—32no—
609C42—32no—
610C42—241no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3C2×#12111yescharacteristic
619C22×C3D4211yescharacteristic
620C22×C3#54611yescharacteristic
621C22×C3#57511yescharacteristic
622C22×C3#57511yescharacteristic
623C22×C3#57611yescharacteristic
624C22×C3#57711yescharacteristic
625C2×D3—41no—
626C2×D3—42no—
627C2×D3—41no—
628C2×D3—42no—
629C2×D3—41no—
630C2×D3—42no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C2×D3—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C3×C4—41no—
647C3×C4—42no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4#53211yescharacteristic
652C3×C4#54011yescharacteristic
653C3×C4D4211yescharacteristic
654C3×C4#55011yescharacteristic
655Dic3—22no—
656Dic3—22no—
657Dic3—41no—
658Dic3—42no—
659Dic3—81no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—61no—
668C23—61no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—62no—
673C23—61no—
674C23—61no—
675C23—121no—
676C23—121no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23C2×D3×D411yescharacteristic
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—62no—
694D4—62no—
695D4—124no—
696D4—121no—
697D4—121no—
698D4—121no—
699D4—121no—
700D4—121no—
701D4—121no—
702D4—244no—
703D4—244no—
704D4—244no—
705D4—244no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—62no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—244no—
745C2×C4C2×D3×D411yescharacteristic
746C2×C4C2×D3×D411yescharacteristic
747C2×C4#100411yescharacteristic
748C2×C4D3×#4111yescharacteristic
749C2×C4D3×#4111yescharacteristic
750C2×C4#100911yescharacteristic
751C8—22no—
752C8—41no—
753C8—62no—
754C8—62no—
755C2×C3—81no—
756C2×C3#242811yescharacteristic
757C2×C3#305411yescharacteristic
758C2×C3#306211yescharacteristic
759C2×C3#327311yescharacteristic
760C2×C3#327511yescharacteristic
761C2×C3#332211yescharacteristic
762C2×C3#332611yescharacteristic
763D3—81no—
764D3—82no—
765D3—161no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—122no—
778C22—121no—
779C22—122no—
780C22—121no—
781C22—121no—
782C22—122no—
783C22—241no—
784C22—241no—
785C22—241no—
786C22—241no—
787C22—241no—
788C22—241no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22#559011yescharacteristic
795C22D3×#12111yescharacteristic
796C22#565411yescharacteristic
797C22#576211yescharacteristic
798C22#576911yescharacteristic
799C22#577711yescharacteristic
800C22#577711yescharacteristic
801C4—41no—
802C4—42no—
803C4—62no—
804C4—62no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—121no—
809C4—122no—
810C4—241no—
811C4#559911yescharacteristic
812C4#560911yescharacteristic
813C4#566311yescharacteristic
814C4#566811yescharacteristic
815C3#2539011yescharacteristic, complemented, Sylow
816C2—81no—
817C2—241no—
818C2—242no—
819C2—481no—
820C2#7690311yescharacteristic
821C2#8006211yescharacteristic
822C2#8024311yescharacteristic
823C2#8066111yescharacteristic
824C2#8090311yescharacteristic
825C2#8143411yescharacteristic
826C2#8154811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2035C2
socleC23×C3C22×D4
hypercenter#2035D3
hypocenterC3#25390
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #82779C2semidirect
2. C2×#5049C2semidirect
3. C2×#4865C2semidirect
4. C2×#4819C2semidirect
5. C2×#4729C2semidirect
6. #73933C2semidirect
7. C3×#2035C2semidirect
8. #70564C2semidirect
9. #70272C2semidirect
10. #70271C2semidirect
11. #70226C2semidirect
12. #69961C2semidirect
13. #69517C2semidirect
14. #68822C2semidirect
15. #68780C2semidirect
70. #2035D3semidirect
160. Dic3⋊C8D4semidirect
164. #809D4semidirect
815. C3#25390semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#827792
C2×#50492
C2×#48652
C2×#48192
C2×#47292
#739332
C3×#20352
#705642
#702722
#702712
#702262
#699612
#695172
#688222
#687802
#253903